Problem 28 · 2009 Math Kangaroo
Stretch
Fractions, Decimals & Percents
percent-multiplier
I have a 6 cm × 6 cm square and a certain triangle. If I lay the square on top of the triangle I can cover up to 60% of the area of the triangle. If I lay the triangle on top of the square I can cover up to 23 of the area of the square. What is the area of the triangle?
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Answer: D — 40 cm²
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Hint 1 of 2
The largest possible overlap of square and triangle is one quantity seen two ways.
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Hint 2 of 2
Set 60% of the triangle equal to 2/3 of the square and solve.
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Approach: equate the maximum overlap from both views
- The square has area 36, so 2/3 of it is 24 - the most the shapes can share.
- From the triangle's side that same maximum is 60% of its area: 0.6 x T = 24, so T = 40.
- The triangle's area is 40 cm^2.
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